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You basically create a dnszone for the other domain.
In this case, as you have two domains on the same subnet, you could create all the information for a domain on the same DNS server, then allow zone transfers. On the other domain, configure a new secondary zone and point it at the server that holds the information. Only need to maintain one set of data then - rather than two copies of the DNS zone.

You need to create a primary zone of externalname.com
Then put the MX records, hosts etc in to that zone. As you are creating a zone for that domain, it will also have to include any external hosts - web sites, ftp sites etc.